from manim import *



class math1(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(6*2+1):       
            dot1=Dot([-50,5*(i-6),0]).set_opacity(0.5)
            dot2=Dot([50,5*(i-6),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(10*2+1):        
            dot3=Dot([(i-10)*5,-30,0]).set_opacity(0.5)
            dot4=Dot([(i-10)*5,30,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        text = Tex(r"\text{设函数}$\int _{0}^{x}f\left( t\right) dt$\text{在}$\left[ 0,1\right] $\text{上二阶导数连续,}$\int _{0}^{1}f\left( x\right) dx=1,\int _{0}^{\frac{1}{2}}f\left( x\right)  >\dfrac{1}{4}$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0)
        text1 = Tex(
                   r"\text{(1)存在}$\xi \in \left( 0,1\right) ,$\text{使得}$f'\left( \xi \right)  <2$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-20,-5,0])
        text2 = Tex(
                    r"\text{(2)若当}$0 <x <1$\text{时,}$f'\left( x\right) \neq 2,$\text{则}$\int _{0}^{x}f\left( t\right) dt >x^{2}$"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-11,-10,0])
        text3 = Tex(
                   r"\text{,证明：}"
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text,RIGHT,buff=1)

        self.play(Write(text),self.camera.frame.animate.scale(0.8),Write(text1),Write(text2),Write(text3))
        self.wait()
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        self.play(text.animate().move_to([0,20,0]),text1.animate().move_to([-20,15,0]) ,text2.animate().move_to([-11,10,0]),text3.animate().move_to([44,20,0]) )
        text40 = Tex(r"\text{!}",color=PURE_RED
                   ,tex_template=TexTemplateLibrary.ctex).scale(20.0).move_to([30,-10,0])
        self.play(Create(text40))
        #透明框框扩展
        #半透明矩阵扩展
        rectangle=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-25,20,0])
        self.play(
            rectangle.animate.stretch(10.0,dim=0)
            
        )

        #曲线箭头
        # 创建一个带有箭头的曲线，让箭头向上凸
        curved_arrow = CurvedArrow(
            start_point=[-25, 22, 0],  # 起始点坐标
            end_point=[-15, 25, 0],  # 终止点坐标
            angle=-PI/4,  # 弯曲的弧度，向上凸
            tip_shape=StealthTip,  # 箭头类型
            color=BLUE,
            stroke_width=20 
        )
         # 缩放箭头头部
        curved_arrow.tip.scale(10)
        
        # 添加到场景中并播放动画
        self.play(Create(curved_arrow))

        #文本
        text4 = Tex(r"\text{触发}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-30,25,0])
        text5 = Tex(r"$F\left( x\right) =\int _{0}^{x}f\left( t\right) dt$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0, 25, 0])
        self.play(Create(text4),Create(text5))
        #直箭头

        #箭头引出+文本
        arrow = Arrow(start=[11,25,0],end=[16,25,0], color=RED
                       , stroke_width=20, tip_length=1)
        self.play(Create(arrow))

        text6 = Tex(r"$F^{'}\left( x\right) =f\left( x\right),F\left( 0\right) =0  $",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30, 25, 0])
        self.play(Create(text6))

        #半透明矩阵扩展
        rectangle1=Rectangle(color=BLUE,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([23,20,0])
        self.play(
            rectangle1.animate.stretch(33.0,dim=0)
        )
        text7 = Tex(r"$F\left( 1\right) =1,F\left( \dfrac{1}{2}\right)  >\dfrac{1}{4}$",color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(rectangle1,DOWN,buff=1)
        self.play(Create(text7))
        #半透明矩阵扩展
        rectangle2=Rectangle(color=YELLOW,fill_opacity=0.5,width=1,height=2.8
                            ,stroke_color=YELLOW,stroke_width=0).move_to([-7,15,0])
        self.play(
            rectangle2.animate.stretch(10.0,dim=0)
        )

        #箭头引出+文本
        arrow1 = Arrow(start=[-5,13,0],end=[-5,0,0], color=RED
                       , stroke_width=20, tip_length=1)
        self.play(Create(arrow1))
        text9 = Tex(r"\text{升维}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0, 5, 0])
        self.play(Create(text9))

        text8 = Tex(r"$ G\left( x\right) =f\left( x\right) -2x$"+
                    r"\text{即证}$G'\left( \xi \right)  <0$"
                    ,color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-5, -1, 0])
        self.play(Create(text8))
       #########################
        arrow2 = Arrow(start=[-5,-3,0],end=[-5,-10,0], color=RED
                       , stroke_width=20, tip_length=1)
        self.play(Create(arrow2))
        text10 = Tex(r"\text{升维}",color=YELLOW
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0, -6, 0])
        self.play(Create(text10))

        text11 = Tex(r"$ H\left( x\right) =F\left( x\right) -x^{2}$"+
                    r"\text{即证}$H''\left( \xi \right)  <0$"
                    ,color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-5, -12, 0])
        self.play(Create(text11),FadeOut(text40))

        #框框
        rectangle3=Rectangle(color=BLUE,fill_opacity=0.0,width=10,height=3
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle3.move_to([39, 25, 0])
        rectangle4=Rectangle(color=BLUE,fill_opacity=0.0,width=25,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle4.move_to([24, 15, 0])
        
        self.play(Create(rectangle3),Create(rectangle4))
        #箭头
        arrow3 = Arrow(start=[34,12,0],end=[34,0,0],color=RED
                       , stroke_width=20, tip_length=1)

        self.play(GrowArrow(arrow3))
        #文本
        text12 = Tex(r"$H\left( 0\right) =0 $"
                    ,color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30, -5, 0])
        text13 = Tex(r"$H\left( 1\right) =0$"
                    ,color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30, -10, 0])
        text14 = Tex(r"$H\left( \dfrac{1}{2}\right)  >0$"
                    ,color=GREEN
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([30, -15, 0])
        self.play(Create(text12),Create(text13),Create(text14))
        self.wait()
